Date of Award
Doctor of Philosophy (PhD)
Dr. R.M. Korol
Dr. F.A. Mirza
Conical steel shells are fairly widely used as elevated water tanks. However, the current code of practise in North America for the design of such reservoir structures provides an obsolete method for ascertaining their adequacy to resist hydrostatic loadings. Moreover, there are no provisions available for handling liquid-filled conical tanks subjected to seismic forces. The lack of appropriate design methods could not have been demonstrated more vividly when in December of 1990, an elevated conical water tower failed by buckling when being filled for the first time. The steel vessel, located in Fredericton, New Brunswick, is claimed to have "exploded" by eyewitnesses.
The work of this thesis, then, was motivated by this failure. It involves non-linear stability analysis of liquid-filled conical steel vessels possessing geometric imperfections and residual stresses, and which can be subjected to hydrostatic and seismic loading. To achieve this, a finite element formulation is developed based on a consistent shell element which is free from spurious shear modes known to exist in the isoparametric shell elements. The consistent shell element employed also exhibits excellent performance in the analysis of plates and shells in the small displacement range. This element is extended to include both geometric and material non-linearities as well as non-linear dynamic analysis. The non-linear finite element model developed is general and can be applied to any thin or thick shell problem. Numerical testing of the non-linear model through static and dynamic analysis of different plate and shell problems indicates the continued excellent performance of the consistent shell element in the non-linear range.
Hydrostatically loaded conical steel vessels are modelled using the consistent shell element. Static stability analyses of conical shells with different geometric imperfection patterns are undertaken and the results indicate that the presence of axisymmetric imperfections leads to the lowest limit load for the structure. The sensitivity of the hydrostatically loaded conical vessels to geometric imperfections and residual stresses is investigated by considering three cases: (i) analysis of perfect vessels, (ii) same as case (i) but with axisymmetric geometric imperfections of the order of the thickness of the shell, (iii) same as case (ii) but with the addition of residual stresses due to welding. The results from these analyses indicate that the liquid-filled conical shells are significantly sensitive to geometric imperfections, and that yielding precedes elastic buckling for tanks having practical dimensions.
The non-linear dynamic (stability) analysis of elevated liquid-filled conical vessels subjected to both horizontal and vertical accelerations, but free from rocking motion, is then considered. The boundary integral method is used to formulate the fluid added-mass matrix resulting from the impulsive component of the hydrodynamic pressure. This is added to the mass matrix of the shell structure to perform free vibration as well as nonlinear time history analyses for elevated liquid-filled conical tanks treated as either perfect or axisymmetrically imperfect. Tanks with different dimensions and imperfection levels are subjected to an appropriately scaled real input ground motion. Some of these elevated structures exhibit inelastic behaviour and generally develop a localized buckle near the bottom of the vessel which leads to the overall instability of the structure. In general, time history analyses indicate that liquid-filled conical tanks, often possessing apparently adequate safety factors under hydrostatic loading, may not be safe under seismic loading. Therefore, a proper modelling procedure along with time dependent analysis must be followed in order to design such tanks safely. The finite element model developed in this thesis is a means provided for such a purpose.
Damatty, Ashraf El, "Non-Linear Dynamic Extension of Consistent Shell Element and Analyses of Liquid-Filled Conical Tanks" (1995). Open Access Dissertations and Theses. Paper 1782.